| 词条 | 复变函数及应用 |
| 释义 | 图书信息书 名: 复变函数及应用（英文版）作 者：（美）布朗 出版社： 机械工业出版社 出版时间： 2009-3-1 ISBN: 9787111253631 开本： 16开 定价: 65.00元 内容简介本书初版于20世纪40年代，是经典的本科数学教材之一，对复变函数的教学影响深远，被美国加州理工学院、加利福尼亚大学伯克利分校、佐治亚理工学院、普度大学、达特茅斯学院、南加州大学等众多名校采用。 本书阐述了复变函数的理论及应用，还介绍了留数及保形映射理论在物理、流体及热传导等边值问题中的应用。 新版对原有内容进行了重新组织，增加了更现代的示例和应用，更加方便教学。 图书目录Preface 1 Complex Numbers Sums and Products Basic Algebraic Properties Further Properties Vectors and Moduli Complex Conjugates Exponential Form Products and Powers in Exponential Form Arguments of Products and Quotients Roots of Complex Numbers Examples Regions in the Complex Plane 2 Analytic Functions Functions of a Complex Variable Mappings Mappings by the Exponential Function Limits Theorems on Limits Limits Involving the Point at Infinity Continuity Derivatives Differentiation Formulas Cauchy-Riemann Equations Sufficient Conditions for Differentiability Polar Coordinates Analytic Functions Examples Harmonic Functions Uniquely Determined Analytic Functions Reflection Principle 3 Elementary Functions The Exponential Function The Logarithmic Function Branches and Derivatives of Logarithms Some Identities Involving Logarithms Complex Exponents Trigonometric Functions Hyperbolic Functions Inverse Trigonometric and Hyperbolic Functions 4 Integrals Derivatives of Functions w(t) Definite Integrals of Functions w(t) Contours Contour Integrals Some Examples Examples with Branch Cuts Upper Bounds for Moduli of Contour Integrals Antiderivatives Proof of the Theorem Cauchy-Goursat Theorem Proof of-the Theorem 5 Series 6 Residues and Poles 7 Applications of Residues 8 Mapping by Elementary Functions 9 Conformal Mapping 10 Applications of Conformal Mapping 11 The Schwarz-Chrstoffer Transformation 12 Integral Formulas of the Poisson Type Appendixes Index |
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